You CAN remove all of the salt from water, how else would chemists do their experiments? Most of the water on the planet has salt in it. I have worked in labs in college doing experiments that depend on the water being as close to 100% pure as possible. Many chemical reactions will NOT take place if the reagent is contaminated with anything, including salt. That being said many reagents are diluted with water to make different molarities (M) ie 110 M hydrochloric acid vs. 2 M hydrochloric acid. How do you decrease M? add water.
I pick up pennies.